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©Tmail Jananam.
®Theebgar creation 2003
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Kjd;ik
vz;fs;.
[Prime Numbers] .03
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Kd;du;
$wpatw;iw tpupthfTk; Nfhit tbtpYk; ghu;g;Nghk;.
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Kjd;ik vz;zh vd;W fhzNtz;ba vz;iz
vd;Nghk;. gpupj;J ghu;f;Fk; vz;iz y
vd;Nghk;. Kjd;ik
vz;zh vdg;ghu;g;gjw;F x
ia y
My; (x-1)
tiu tFj;J ghu;j;jy; Ntz;Lk;. mjhtJ y
= 2 --> (x-1)
vdNt x
Kjd;ik vz;zhf ,Ug;gjw;F balance of (
x / y ) = m
vdpd;
m
not = 0 Mf ,Uj;jy; Ntz;Lk;.
Kiw 01.
vz;iz Kjypy;
2 My; tFj;jy;. mg;NghJ kPjp ngwg;gl;lJ vdpy; mjhtJ m
= 0 me;j
vz; Kjd;ik vz;zhf vd;gjw;F ,Uf;fKbahJ. ,g;NghJ y
= 2.
x ,w;F 2 fhuzpahf ,Uf;fKbahJ vd;gjhy; mt;thW vdpd;
,dp y = 2 --> (x-1)/2
tiu gpupj;J ghu;j;jhy; NghJkhdJ.
cjhuzkhf
x = 17
Mf y
= 2 -->( 17-1) mjhtJ
y
= 2 -->16 vdNt gpd;tUkhW mikAk;.
- 1tJ jlit
y = 2 Mf m = 1
,g;NghJ y
= 2 -->( 17-1)/2 mjhtJ
y
= 2 -->8
- 2tJ jlit
y = 3 Mf m = 2
- 3tJ jlit
y = 4 Mf m = 1
- 4tJ jlit
y = 5 Mf m = 2
- 5tJ jlit
y = 6 Mf m = 5
- 6tJ jlit
y = 7 Mf m = 3
- 7tJ jlit
y = 8 Mf m = 1
,jw;F NkYk; tFf;f Njit ,y;iy. mjhtJ
16 tiu tFf;f Njit ,y;iy.
,uz;L xU fhuzp ,y;iy vd;why; me;j vz;iz me;j vz;zpd; miug;gq;F
tiu cs;s vz;fshy; tFj;jhy; NghJkhdJ.
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vz; x
vd;f
balance of (x/2) not= 0 vd;why;
x/2 tiuAs;s
vz;fspdhy; x
ia tFj;jhy; NghJkhdJ.
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Kiw
02
Kjypy; ,uz;bw;F $wpatop Kiw midj;J vz;fspw;Fk; nghUe;Jk; vd;gjhy;
mt;ntz;zpd; tu;f;f %yk; tiuAs;s vz;fspdhy; tFj;jhy; NghJkhdJ.
mjhtJ Xu; vz;zpw;F tu;f;f %yj;jpYk; ngupa fhuzp ,Uf;Fnkdpd;
tu;f;f %yj;jpYk; rpwpa fhuzp ,Uf;Fk;;. cjhuzkha;
cjhuzkhf
x = 17
Mf y =
2 -->( 17-1) mjhtJ
y
= 2 -->16 vdNt gpd;tUkhW mikAk;.
step 01
- 1tJ jlit
y = 2 Mf m = 1
,g;NghJ y
= 2 -->( 17-1)/2 mjhtJ
y
= 2 -->8
- 2tJ jlit
y = 3 Mf m = 2
,g;NghJ y
= 2 -->( 17-1)/3 mjhtJ
y
= 2 -->5
- 3tJ jlit
y = 4 Mf m = 1
- 4tJ jlit
y = 5 Mf m = 2
Mdhy;
step
02
- 1tJ jlit
y = 2 Mf m = 1
,g;NghJ y
= 2 -->( 17-1)/2 mjhtJ
y
= 2 -->8
- 2tJ jlit
y = 3 Mf m = 2
,g;NghJ y
= 2 -->( 17-1)/3 mjhtJ
y
= 2 -->5
- 3tJ jlit
y = 4 Mf m = 1
,g;NghJ y
= 2 -->( 17-1)/4 mjhtJ
y
= 2 -->4
,jw;F
NkYk; tFf;f Njit ,y;iy. mjhtJ 5 tiu tFf;f Njit ,y;iy.
vdNt ,k;KiwahdJ midj;J vz;fspw;Fk;
gpd;gw;wg;glyhk; vd;gjhy; me;j vz;zpd; tu;f;f %yk; tiuAs;s
vz;fspdhy; tFj;jhy; NghJkhdJ. Vnddpy; tu;f;f%yj;ij tpl ngupa
fhuzp ,Uf;f Ntz;Lnkdpd; tu;f;f %yj;ij tpl rpwpa fhuzpAk;
,Uf;f Ntz;Lk;. Vnddpy; tu;f;f %yk;jhd; ,uz;Lk; rkdhd fhuzpfspdhdJ.
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vz;
x
vd;f
Öx
tiuAs;s vz;fspdhy; tFj;jhy;
NghJkhdJ.
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Kiw
03
,uz;L Xu; fhuzp ,y;iy vdpd; ,uz;bd; klq;FfSk; fhuzpaha; mikahJ.
mjhtJ ,uz;L Xu; fhuzp ,y;iy vdpd;;; 4> 6 Nghd;wdTk; fhuzpaha;
mikaKbahjd.
vdNt fhuzpahf xw;iw vz;fNs mikaKbAkhjyhy; ,uz;bw;F mLj;j xw;iw
vz;zhd %d;wpypUe;J xt;nthU xw;iw vz;zhf mjhtJ
3+2, (3+2)+2 Mf Öx
tiu tFj;jhy; NghJkhdJ. |
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vdNt
,uz;bw;Fg; gpd; %d;why; tFj;Jg; ghu;j;jgpd; 3+2,
5+2 mjhtJ
current
number = current number + 2
Mf tFj;jhy; NghJkhdJ.
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,jw;Fupa fl;lisfs; njhlu;e;J.... |
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njhlUk;..........
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thd; ,af;ftpay;